A new three-triangle based method to linearly concave hydropower output in long-term reservoir operation

Zheng, Hao; Feng, Suzhen; Chen, Cheng; Wang, Jinwen

doi:10.1016/j.energy.2022.123784

Cited by 6 publications

(4 citation statements)

References 38 publications

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“…where V it demonstrates storage in hm 3 of reservoir i at the beginning of time t; Ω(i) means the set of reservoirs immediately upstream of reservoir i; Q it is the outflow in m 3 /s in time t from reservoir i; I it represents local inflow in m 3 /s into reservoir i in time t; ∆t is the number of days in time t; V i ini and V i end denote initial and target storages in hm 3 at the beginning and end of the planning horizon, respectively; spl it means the spillage in m 3 /s in time t from reservoir i; q it is generating discharge in m 3 /s in time t from plant i.…”

Section: Problem Formulationmentioning

confidence: 99%

“…The hydro scheduling of cascaded reservoirs presents a complex optimization problem characterized by an extensive system scale, diverse objectives, high dimensionality, and varying regulation performance of reservoirs [2]. Additionally, it requires accounting for nonlinearities with a dynamic water head, stochastic inflow, and upstream-downstream relationship between upstream and downstream hydropower plants [3]. Hence, it is very important to have an effective and efficient approach or methodology to tackle the monthly hydropower scheduling problem, which aims to maximize comprehensive benefits while considering various boundary conditions and constraints [4].…”

Section: Introductionmentioning

confidence: 99%

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A Special Ordered Set of Type 2 Modeling for a Monthly Hydropower Scheduling of Cascaded Reservoirs with Spillage Controllable

Liu,

Qian,

et al. 2023

Water

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This study introduces a novel approach for optimizing the monthly hydropower scheduling of cascaded reservoirs by employing a special ordered set of type 2 (SOS2) formulation within a mixed integer linear programming (MILP) model. The proposed method linearizes the relationships between hydropower output, spillage, storage, and outflow, enabling controllable spillage. The objective is to minimize spillage, maximize firm hydropower output, and maximize energy production, all in priority while considering complex constraints such as reservoir storage and discharge bounds, upstream–downstream relationship, and water balance. The approach is applied to four cascaded reservoirs on the Lancang River. Results indicate that the SOS2 formulation effectively minimizes spillage, maximizes hydropower generation, and ensures maximum firm power output. Comparisons across different gridding resolutions reveal that more grid points yield greater benefits but with a longer solution time. Furthermore, a comparison with the Successive Quadratic Programming (SQP) method highlights the superior performance of the SOS2 model in terms of objective improvement and solution efficiency. This research offers valuable insights into optimizing monthly hydropower scheduling for cascaded reservoir systems, enhancing operational efficiency and decision-making in water resources management.

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Section: Problem Formulationmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

A Special Ordered Set of Type 2 Modeling for a Monthly Hydropower Scheduling of Cascaded Reservoirs with Spillage Controllable

Liu,

Qian,

et al. 2023

Water

Self Cite

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“…Generally, researches on the optimal scheduling of cascaded reservoirs typically encompass several objectives, including maximizing hydropower efficiency [1,2], mitigating flood risks [3,4], and fulfilling ecological requirements [5,6]. The challenge lies in the highly nonlinear nature of this problem at the physical level, where the coupling between cascaded reservoirs, the stochasticity of inflows, and the calculation of head differentials introduce numerous difficulties in solving the optimal scheduling problem for cascaded reservoirs [7,8].…”

Section: Introductionmentioning

confidence: 99%

Water Supply Strategy of Cascade Reservoirs for Irrigation and Industrial Uses Based on Marginal Benefit

Feng,

Wang

2024

E3S Web Conf.

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The operation of reservoir is to optimize the utilization of water resources and bring its maximum benefit. Most studies of reservoir scheduling generally pursue the maximization of revenue, and rarely consider the demand of water supply from reservoirs to agriculture or factories in the scheduling process. The few studies that have taken this into account have included this demand in the objective function or constraint, rather than in terms of marginal benefits. This work presents a method to determine water supply decision of reservoir based on marginal benefit. By iteratively linearizing the cascaded reservoir scheduling model and calculating the optimal solution to the dual problem of the model, this method provides a reference for the water supply plan of reservoir to agricultural departments and factories. The proposed method has been applied to 8 reservoirs on the Jinsha River cascade. Convergence in water head is achieved after 15 iterations, and numerical comparisons of the marginal value of water resources at different locations and periods across various reservoirs are obtained.

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“…The linear programming (LP), for instance, was employed by Feng et al [5] who presented a weekly hydropower scheduling problem of cascaded hydropower plants that was formulated into a mixed integer linear programming (MILP) model. Formulating a nonlinear optimization into an LP problem, however, is a skillful task, requiring the nonlinear functions to be linearized, as illustrated by Zheng et al [6], who presented a new three-triangle based method to linearly concave the hydropower output function (HOF), or in many cases, many integer variables to be introduced, causing the "combinatorial explosion" that makes it unlikely to derive a satisfactory solution in reasonable time. Nonlinear programming (NLP) is also a popular option, as applied by Barros et al [7], who formulated hydropower generation into a nonlinear function of the water discharge and head, but it could not guarantee a global optimum.…”

Section: Introductionmentioning

confidence: 99%

A Monthly Hydropower Scheduling Model of Cascaded Reservoirs with the Zoutendijk Method

Zhou¹,

Feng

et al. 2022

Water

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A monthly hydropower scheduling determines the monthly flows, storage, and power generation of each reservoir/hydropower plant over a planning horizon to maximize the total revenue or minimize the total operational cost. The problem is typically a complex and nonlinear optimization that involves equality and inequality constraints including the water balance, hydraulic coupling between cascaded hydropower plants, bounds on the reservoir storage, etc. This work applied the Zoutendijk algorithm for the first time to a medium/long-term hydropower scheduling of cascaded reservoirs, where the generating discharge capacity is handled with an iterative procedure, while the other head-related nonlinear constraints are represented with exponential functions fitting to discrete points. The procedure starts at an initial feasible solution, from which it finds a feasible improving direction, along which a better feasible solution is sought with a one-dimensional search. The results demonstrate that the Zoutendijk algorithm, when applied to six cascaded hydropower reservoirs on the Lancang River, worked very well in maximizing the hydropower production while ensuring the highest firm power output to be secured.

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A new three-triangle based method to linearly concave hydropower output in long-term reservoir operation

Cited by 6 publications

References 38 publications

A Special Ordered Set of Type 2 Modeling for a Monthly Hydropower Scheduling of Cascaded Reservoirs with Spillage Controllable

A Special Ordered Set of Type 2 Modeling for a Monthly Hydropower Scheduling of Cascaded Reservoirs with Spillage Controllable

Water Supply Strategy of Cascade Reservoirs for Irrigation and Industrial Uses Based on Marginal Benefit

A Monthly Hydropower Scheduling Model of Cascaded Reservoirs with the Zoutendijk Method

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